How can I take greater control of subdomain management?

I have an SS at www.mysite.co.uk and want to maintain that, but also host an entirely separate (React + Firebase) site at, say, mysubdomain.mysite.co.uk, but this doesn't seem possible with the subdomain controls SS offers. Therefore I'm wondering if I can do one of the two following things (or possibly other suggestions if you have them):

1. log into Tucows myself to administrate my own DNS etc. stuff; and/or 
2. transfer away from SS (as per the link listed below) and thereafter administrate my own DNS etc. stuff myself?

https://support.squarespace.com/hc/en-us/articles/205812338-Transferring-a-domain-away-from-Squarespace

Thank you for taking the time to read

jbm

I haven't read this article myself yet but it might help: https://support.squarespace.com/hc/en-us/articles/215744668-Pointing-a-Squarespace-Domain#toc-point-a-squarespace-subdomain